Paul, you wrote: "a short training interval from 1993 to 2001 can recreate the rest of the time series"
This is valid if the QBO training interval is not some sort of singularity, like the Feynman Point in the expansion of pi. A quasi-periodic series is at best only simulated, not fully recovered, from a short data sample.
There is a middle ground between the "climate science guardians" not seeing any lunar forcing, and your position of solely seeing lunar forcing. This disagreement represents incomplete explanations on both sides. The Guardians do see a probable solar "quasi-biannual" signal, but with a slipping glitch, like worn gears. I see both Lunar and Solar semi-forcing, from heuristic logic, with no exclusive-or (XOR) dependence.
Can we not entertain a notion of multi-forcing, where various factors multi-chaotically alternate? If "correlation does not imply causation", where is proof of causation as tidal forcing? QBO statistics are not precise enough to exactly match to tidal periods without a lot of noise to confound final existence proof.
A known tidal effect on wind is a velocity maxima during high tide, caused by rising water squeezing wind upward, essentially a Venturi Effect. Conversely, there is a wind velocity minima during low tide. This oscillation is often masked by other weather system variables, but Sailors have long been aware of the effect, and its in the data. No doubt real-time QBO is slightly sensitive to this tidal effect propagating all the way up to the Stratosphere, over ocean. What part is harmonic forcing or asynchronous with QBO is another question.
Late-night early-morning surface level inversion layers also squeeze wind upwards, typically to a far greater magnitude. Like chaotically breaking dawn waves in the upper stratosphere, this is bound to be a cause of QBO noise. There is also annual precession wobble pummeling QBO north and south with Rossby-Hadley cells.